Find the slope of the line that contains the two points (3,2) and (1,-4).
m = - 3
m = - 1/3 <-- ?
m = 3
m = 1/3
Find the slope of the line that contains the points (-2, 4) and (-4, 6).
m = -1
m = 1 <--
m = - 1/3
m = 1/3
Find the equation of the line that passes through the points (7,4) and (-5,-2)?
y=1/2x-1/2
y=-1/2x-1/2
y=-1/2x+1/2<--
y=1/2x+1/2
Find the equation of the line that passes through the points (1,4) and (2,-8).
y = -3x + 9
y = 6x + 5
y = -12x + 16
y = 12x - 8 <---
1. (3,2), (1,-4)
m = (y2-y1)/(x2-x1) = (-4-2)/(1-3) = -6/-2 = 3.
2. (-2,4), (-4,6).
m = (6-4)/(-4-(-2)) = 2/-2 = -1.
3. (7,4), (-5,-2).
m = (-2-4)/(-5-7) = -6/-12 = 1/2.
Y = mx + b
4 = (1/2)7 + b, b = 1/2.
Y = (1/2)x + 1/2.
4. (1,4), (2,-8).
m = (-8-4)/(2-1) = -12,
Y = mx + b.
4 = -12*1 + b, b = 16.
Y = -12x + 16.
To find the slope of a line that contains two points, you can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two given points.
For the first question:
Given points: (3, 2) and (1, -4)
Using the formula, we can calculate the slope:
m = (-4 - 2) / (1 - 3)
m = (-6) / (-2)
m = 3
So, the slope of the line is 3.
For the second question:
Given points: (-2, 4) and (-4, 6)
Using the formula, we can calculate the slope:
m = (6 - 4) / (-4 - (-2))
m = 2 / (-2)
m = -1
So, the slope of the line is -1.
For the third question:
Given points: (7, 4) and (-5, -2)
Using the formula, we can calculate the slope:
m = (-2 - 4) / (-5 - 7)
m = (-6) / (-12)
m = 1/2
So, the slope of the line is 1/2.
For the fourth question:
Given points: (1, 4) and (2, -8)
Using the formula, we can calculate the slope:
m = (-8 - 4) / (2 - 1)
m = (-12) / (1)
m = -12
So, the slope of the line is -12.
Now, to find the equation of the line passing through two points, you can use the point-slope form:
y - y1 = m(x - x1)
where (x1, y1) is one of the points on the line and m is the slope.
For the third question:
Using the point (7, 4) and slope 1/2, the equation becomes:
y - 4 = (1/2)(x - 7)
Simplifying, we get:
y - 4 = (1/2)(x) - (1/2)(7)
y - 4 = (1/2)x - 7/2
y = (1/2)x - 7/2 + 4
y = (1/2)x - 7/2 + 8/2
y = (1/2)x + 1/2
So, the equation of the line passing through (7, 4) and (-5, -2) is y = (1/2)x + 1/2.
For the fourth question:
Using the point (1, 4) and slope -12, the equation becomes:
y - 4 = (-12)(x - 1)
Simplifying, we get:
y - 4 = -12x + 12
y = -12x + 12 + 4
y = -12x + 16
So, the equation of the line passing through (1, 4) and (2, -8) is y = -12x + 16.